We continue by comparing the outage of the TVAD channel and its twirled approximated channels. Figure REF  plots the hashing outage probability results of the TVADPTA and TVADCTA channels. Note that the x-axis is still \(\gamma \) , despite the fact that the defining parameter for the TVADPTA and TVADCTA channels is \(\mathbf {p}\) . However, the \(\gamma \)  associated to a given \(p\)  can be obtained easily [1]}, which is necessary to perform comparisons with the TVAD channel. The quantum outage capacities of the TVAD channel from figure REF  are also shown. Note that the hashing outage probabilities for the ADPTA and ADCTA channels are worse than the quantum outage probability of the TVAD channel, since the noise limits for those channels are lower than the one for the TVAD. This means that the hashing outage probabilities of the twirled channels are worse because their noise limits are worse, and not because they are more sensitive to time-fluctuations. This is analogous to the previous explanation on the difference between the values of \(p_{\mathrm {out}}^\mathrm {Q}\)  for QECCs with different quantum rates operating over the TVAD channel. Also note that even though the hashing outage probabilities for these approximated channels are higher than the quantum outage probability for the TVAD, one can not conclude that the actual quantum outage probability for these twirled channels will be worse than the one for the AD channel (recall that the hashing outage probability provides an upper bound on the actual outage probability).
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